What length of bolt is needed to fasten two pieces of metal each 3/5 inch thick, if a 3/16 inch lock washer is used and a 1/8 inch nut is used?
Answer (2)
Calculate the total thickness of the two metal pieces: 2 × 5 3 = 5 6 .
Add the thickness of the lock washer: 5 6 + 16 3 = 80 111 .
Add the thickness of the nut: 80 111 + 8 1 = 80 121 .
The required length of the bolt is 80 121 .
Explanation
Understanding the Problem Let's break down this problem. We need to find the total length required for a bolt to pass through two metal pieces, a lock washer, and a nut. We'll add up all the individual thicknesses to find the total length.
Calculating Metal Thickness First, we need to calculate the total thickness of the two metal pieces. Each piece is 5 3 inch thick, so two pieces will be: 2 × 5 3 = 5 6
Adding Lock Washer Thickness Next, we add the thickness of the lock washer, which is 16 3 inch: 5 6 + 16 3 To add these fractions, we need a common denominator. The least common multiple of 5 and 16 is 80, so we convert the fractions: 5 6 = 5 × 16 6 × 16 = 80 96 16 3 = 16 × 5 3 × 5 = 80 15 Now we can add them: 80 96 + 80 15 = 80 111
Adding Nut Thickness Finally, we add the thickness of the nut, which is 8 1 inch: 80 111 + 8 1 We need a common denominator again. We can convert 8 1 to a fraction with a denominator of 80: 8 1 = 8 × 10 1 × 10 = 80 10 Now we can add: 80 111 + 80 10 = 80 121
Final Answer So, the total length of the bolt needed is 80 121 inches.
Examples
When building a deck, you need to fasten the deck boards to the frame. Each board might be a certain thickness, and you'll use washers and nuts to secure them. Calculating the correct bolt length ensures a strong, safe deck. If each board is 3/5 inch thick, you're using a 3/16 inch lock washer and a 1/8 inch nut, you'd need a bolt that's 121/80 inches long to securely fasten everything together.
To fasten two pieces of metal each 5 3 inch thick, along with a lock washer of 16 3 inch and a nut of 8 1 inch, a bolt with a length of 80 121 inches is required. This totals to approximately 1.5125 inches. The calculation involves adding the thicknesses of all components together.
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